Data‑centric scaling of RLVR has relied on gathering or generating verifiable training problems, yet corpus size alone does not guarantee a useful learning signal for a target policy. We model dataset effectiveness as a function of the problem set, the target policy, and the training rollout budget. Empirically, a large open‑source math corpus falls almost entirely into a zero‑advantage trap: for a fixed policy and budget about 88% of problems are either solved in every rollout or fail in every rollout. Filtering concentrates the remaining samples but can only keep the easy ones, discarding the hard problems. Effective synthetic problems must require the reasoning operations and compositions needed for those hard problems, while their difficulty is calibrated so that some rollouts succeed, some fail, and at least one correct solution fits within the budget. Prompting a teacher model to generate harder problems directly does not achieve this. Guided by these principles we introduce MagicBeanStalk, a top‑down decomposition and bottom‑up recursive synthesis algorithm. Starting from a few seed problems, it recursively grows families of new problems that preserve the seeds’ reasoning blueprints and are automatically calibrated to the target policy and budget. Across eight math benchmarks, continual RLVR on MagicBeanStalk problems improves gpt‑oss‑120b from 61.2 to 69.8 (+8.6) and DeepSeek v4Flash from 72.4 to 77.9 (+5.4) under a 16K‑token budget. Training on the full 78K‑problem source corpus yields only +1.1, and the best filtered real‑data subset yields +5.8. In finance, we synthesize over 14K verifiable problems from just 340 solutions, gaining +6.9 on SecQue and +2.4 on FinanceBench.
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